Donald Trump has tweeted an unsubstantiated claim from an hardline Iranian cleric and circulated by a news agency linked to the country’s Revolutionary Guard, that thousands of Iranians were granted US citizenship as part of the 2015 nuclear deal.

In his 8am tweet, the US president said: “Just out that the Obama administration granted citizenship, during the terrible Iran Deal negotiation, to 2,500 Iranians, including to [sic] government officials. How big (and bad) is that?”

He cited no evidence for the allegation.

The Iranian American population is about a million strong, and the number of Iranians naturalised in the US dipped slightly between 2015 and 2016, from 10,344 to 9,507.

The claim of 2,500 Iranians being made US citizens as part of the nuclear deal was first made in a newspaper interview on 26 June with Mojtaba Zonnour, a member of parliament from Iran’s Shia religious centre at Qom. He is an outspoken critic of President Hassan Rouhani and the nuclear agreement, by which Iran curbed its nuclear programme in return for sanctions relief.

Trump walked out of the agreement, the Joint Comprehensive Plan of Action (JCPOA) in May, and Zonnour took part in the burning of a US flag in the parliament in response.

Zonnour told the reformist Iranian daily Etemaad: “When Mr Obama, during the JCPOA negotiations, decided to do a favour to these men [Rouhani and his aides], he granted citizenships to 2,500 Iranians and some officials competed with each other over whose children could be part of these 2,500 people.”

The cleric added: “Today, if the US deports these people, then we will find out who is complicit and sells the national interest like selling candies to America.”

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The semi-official Fars news agency, which is allied to hardline Rouhani opponents and the elite Revolutionary Guards, published a news story focusing on Zonnour’s claim about a citizenship deal. Fars frequently breaks important news due to its access to the intelligence apparatus and military officials.

Fox News picked up the Fars news story on Monday, and Sean Hannity, a fervent Trump supporter and confidante, as well as a Fox new host, tweeted the story as “developing” soon after 1pm the same day.

Trita Parsi, the head of the National Iranian American Council, said:“That a cleric in Iran is throwing out complete conspiracy theories is sadly normal. Right now there is a strong push from hardliners to get Rouhani to resign and accusations of this kind are probably calculated to exploit economic frustration among Iranians.

“What is different now is there is a US president who is repeating these wild accusations.”